Project #48132 - Statistics

28 Mathematics Tutors Online

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

NAME_____________________________

INSTRUCTIONS

·The quiz is worth 40 points total.

·The quiz covers Chapters 4, 5 and 6.

·Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from program software packages will not be accepted.

·The quiz is open book and open notes. This means that you may refer to your textbook, notes, and online course materials, but you must work independently and may not consult anyone. The brief honor statement is on top of the exam. If you fail to put your name under the statement, your quiz will not be accepted. You may take as much time as you wish, provided you turn in your quiz via LEO by 11:59 pm EST on Sunday, November 23.

1. (5 points)Assume that you make random guesses for 5 true-or-false questions.

(a) (3 pts) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)

(b) (2 pts) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”.Are event A and event B independent?Please explain.

2. (6 points) A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster.We also know that 30 students enroll in both courses.

(b) (3 pts) What is the probability that a random selected student takes French class, given that he / she takes Japanese class. (Show work and write the answer in simplest fraction form)

3. (4 points) You are given the following probability distribution:

x

-1

0

1

2

3

P(x)

0.1

0.3

0.4

0.1

0.1

(a)(2 pts) What is the expected value of the probability distribution? (Show work and round the answer to one decimal place)

(b)(2 pts) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)

4. (8 points) Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves.If her opponent serves 10 times, answer the following questions:

(a) (2 pts) Let random number X be the number of returns that Mimi gets. As we know X follows a binomial distribution. Identify the number of trials (n), and probability of success in any one trial (p).

(b) (4 pts) What is the probability that she returns at least 1 of the 10 serves from her opponent? (Show work and round the answer to 4 decimal places)

(c) (2 pts) How many serves can she expect to return? (Hint : What is the expected value?)(Show work and round the answer to 2 decimal places)

5. (8 points) If the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

(a) (2 pts) What is the 75th percentile for the IQ score distribution?

(b) (3 pts) Find the probability that a randomly selected person has an IQ score between 88 and 115. (Show work and round the answer to 4 decimal places)

(c) (3 pts) Find the probability that a sample of 36 random selected people has a mean IQ score greater than 105. (Show work and round the answer to 4 decimal places)

6. (4 points) There are 10 members in the UMUC Stats Club.

(a) (2 pts) The Club must select a president, a vice president and a treasurer for the school year. How many different ways can the officers be selected?(Show work)

(b) (2 pts) The Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. How many different ways can the delegate be selected? (Show work)

7. (5 points) True or False. Justify for full credit.

(a)

(b)If event A and event B are independent,then

(c)If event A and event B are disjoint,then

(d)The probability of an impossible event is 0.

(e)The normal distribution is always symmetric with respect to its mean.